Defining the Standard State Quantifying Activity • Assume that, if the environment remains constant, the • Common Choices for the Environment in the Standard activity of a species is always proportional to its State (the Reference Environment or Reference State) concentration. Then, when comparing the behavior of the –Forgaseous species: The conditions in an ideal gas at a standard same species in two systems, concentration differences temperature and pressure (typically 20o or 25oC and 1.0 atm) account for part of the difference in activity, and any other –Forsolutes in dilute aqueous solutions: Conditions in which each difference in activity is attributed to the environment, i.e: molecule of solute interacts only with water molecules (i.e., infinite dilution in pure water), at the standard T and P; [marine chemists commonly use “standard seawater” rather than pure water as the environ. factor background solution] ccfor i in system a ≡=iiγ –Forwater (or, in general, the main component of any liquid phase): i c environ. factor c ι The conditions in pure water at the standard T and P i,. std state i ,. std state for i in std. state – For the major and minor components of solids: The conditions in a pure solid of that constituent at the standard T and P • The ‘environmental factor’ can be considered the reactivity per molecule or per mole. Thus, the product of the numerators or denominators in the middle expression is (mol/L * reactivity/mol), or reactivity/L.

–Forgases that follow the ideal gas law, c = P /RT,so: G,i i ci ai ≡ γι cPRTP/ cistdstat,. e ii== i cRTistdstate,. 1.0 atm / 1.0 atm •Theactivity coefficient, γi, is the ratio of the activity of a molecule (or mol) of i in the actual –Forsolutes in aqueous solutions: system to the corresponding activity in the c M mol/L standard state i = cistdstate,. 1.0 mol / L –Ifγi =1.0, each molecule of i is as “active” as it would be in its reference state; commonly called “ideal behavior” –Forbulk constituent of a liquid or any constituent of a – Molecules in a given system might be either more or

solid: less active than in the reference state (γi > or < 1.0, ccii x i respectively) ===xi cci,. std state i , pure phase x i, pure phase

1 Activity Coefficients of Dissolved Ions Activity Coefficients of Dissolved Ions

21/2 Debye-Hückel log10(γ D-H )=−AzI

I 1/2 Extended 2 log10 (γ Ext.D-H ) =−Az 1/2 Debye-Hückel 1+ BaI

1/2 2 ⎧ I ⎫ Davies log10 (γ Davies )=−AzI⎨ 1/2 − 0.2 ⎬ ⎩⎭1+ I

Summary: Chemical Activity Conventions in this Course • A quantitative measure of the tendency for molecules to undergo a chemical change that reduces their concentration • Activity of species i: ai or {i} • Incorporates factors related to concentration of the molecule of interest and the environment in which it exists • Molar concentration of species i: ci or [i] • Quantified based on definition of an arbitrary standard state, comprising a standard concentration and a standard • Activity and molar concentration in systems (reference) environment; typically, these conditions are different for species in different phases, and for major vs. where γi =1.0:(i) minor components of an aqueous solution • Standard concentration is typically (but not necessarily) a value of 1.0 with units appropriate to the phase; standard environment is typically close to that under normal conditions at earth’s surface, albeit somewhat idealized • Activity coefficients for solutes can be predicted; activity coefficient for water and gases is usually assumed to be 1.0

2 The Kinetic View of Chemical Equilibrium Molecular Energy According to the • Reactions occur by collisions among molecules Boltzmann Distribution – For molecules in the same (homogeneous) phase, collision frequency should be proportional to the concentrations of the colliding species 0.25 – For molecules in different phases, collision frequency is proportional to the concentrations in the phases (presumed to be 0.20 proportional to the concentrations at the interface) and the Area equals fraction of “concentration” of interface molecules with kinetic energy 0.15 between 3 and 6 kJ/mol – Environmental factors also affect the tendency of a species to

react, so the proper parameter for characterizing reactivity is ai; 0.10 nevertheless, it is common practice to incorporate activity coefficients into other terms and write reaction rates in terms of concentrations (except in one important case, to be shown) 0.05 Probability density density (mol/kJ) Probability

– All reactions are presumed to be reversible 0.00 – Environmental factors captured in activity coefficient – lower activity 03691215 coefficient corresponds to more stability, less reactivity Kinetic energy (kJ/mol)

Molecular Energy Changes Elementary Reactions During a Reaction • Proceed in a single step, in accord with the reaction stoichiometry Molecules above this • Follow a rate law that is established by energy level (defined somewhat arbitrarily) stoichiometry: Chemical are called activated Energy/mol E* complexes A+B→P abAB+ → p P E*P→A+B

Products E Δ rxn b p ab rr= rrPA=− rkccAAAB=− BA Reactants a a

Progression of Reaction (Reaction Note that relationships among r , r , and r apply Coordinate) A B C regardless of whether reaction is elementary.

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